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Kai Lai Chung (traditional Chinese: 鍾開萊; simplified Chinese: 钟开莱; September 19, 1917 – June 2, 2009) was a Chinese American mathematician known for his significant contributions to modern probability theory.

Chung Kai-lai
Chung Kai-Lai.jpg
Born(1917-09-19)September 19, 1917
DiedJune 2, 2009(2009-06-02) (aged 91)
ResidenceChina, United States
NationalityRepublic of China, United States
CitizenshipRepublic of China, United States
Alma materTsinghua University
Princeton University
Known formodern probability theory
Scientific career
InstitutionsTsinghua University
University of Chicago
Columbia University
University of California, Berkeley
Cornell University
Syracuse University
Stanford University
National University of Singapore
Doctoral advisorHarald Cramér
John Wilder Tukey
Doctoral studentsCyrus Derman
J. Michael Steele
Ruth Jeannette Williams


Chung was a native of Hangzhou, the capital city of Zhejiang Province. Chung entered Tsinghua University in 1936, and initially studied physics at its Department of Physics. In 1940, Chung graduated from the Department of Mathematics of the National Southwestern Associated University, where he later worked as a teaching assistant.[1] During this period, he first studied number theory with Lo-Keng Hua and then probability theory with Pao-Lu Hsu.

In 1944, Chung was chosen to be one of the recipients of the 6th Boxer Indemnity Scholarship Program for study in the United States. He arrived at Princeton University on December 1945 and obtained his PhD in 1947. Chung’s dissertation was titled “On the maximum partial sum of sequences of independent random variables” and was under the supervision of John Wilder Tukey and Harald Cramér.[2]

In 1950s, Chung taught at the University of Chicago, Columbia University, UC-Berkeley, Cornell University and Syracuse University. He then transferred to Stanford University in 1961, where he made fundamental contributions to the study of Brownian motion and laid the framework for the general mathematical theory of Markov chains. Chung would later be appointed Professor Emeritus of Mathematics of the Department of Mathematics at Stanford.

Chung was regarded as one of the leading probabilists after World War II. He was an Invited Speaker at the ICM in 1958 in Edinburgh and in 1970 in Nice. Some of his most influential contributions have been in the form of his expositions in his textbooks on elementary probability and Markov chains. In addition, Chung also explored other branches of mathematics, such as probabilistic potential theory and gauge theorems for the Schrödinger equation.

Chung's visit to China in 1979 (together with Joseph L. Doob and Jacques Neveu), and his subsequent visits, served as a point of renewed exchange between Chinese probabilists and their Western counterparts. He also served as an external examiner for several Universities in the Asian region, including the National University of Singapore.

In 1981, Chung initiated, with Erhan Cinlar and Ronald Getoor, the "Seminars on Stochastic Processes", a popular annual national meeting covering Markov processes, Brownian motion and probability.

Chung also possessed a wide-ranging and intimate knowledge of literature and music, especially opera. He also had an interest in Italian culture and taught himself Italian after he retired. Chung spoke several languages and translated a probability book from Russian to English.

Chung died of natural causes on June 1, 2009, at the age of 91.


  • Elementary Probability Theory; by Kai Lai Chung & Farid Aitsahlia; Springer; ISBN 038795578X.
  • A Course in Probability Theory; by Kai Lai Chung.[3]
  • Markov Processes with Stationary Transition Probabilities, by Kai Lai Chung.[4]
  • Selected Works Of Kai Lai Chung; World Scientific Publishing Company; ISBN 981-283-385-4.
  • Green, Brown, & Probability and Brownian Motion on the Line; by Kai Lai Chung; World Scientific Publishing Company; ISBN 981-02-4689-7.
  • Introduction to stochastic integration (Progress in probability and statistics); K. L. Chung and R. J. Williams.
  • Introduction to Random Time and Quantum Randomness; by Kai Lai Chung & Jean Claude Zambrini; World Scientific; ISBN 978-981-238-388-4.
  • Chance & Choice: Memorabilia; Kai Lai Chung.
  • Markov Processes, Brownian Motion, and Time Symmetry; (Grundlehren der mathematischen Wissenschaften); by Kai Lai Chung & John B. Walsh.
  • From Brownian Motion to Schrödinger's Equation; (Grundlehren der mathematischen Wissenschaften); Kai Lai Chung & Zhongxin Zhao.[5]
  • Lectures from Markov Processes to Brownian Motion; (Grundlehren der mathematischen Wissenschaften); by Kai Lai Chung.[6]


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